Update field1.table1 based on compound join between table1 and table2 - Oracle

Question

I want to run update statement on Oracle 11g, but it fails with the following error:

SQL Error: ORA-01427: single-row subquery returns more than one row 01427. 00000 - "single-row subquery returns more than one row"

Here's what I'm trying to do in pseudocode:

Update Table1
Set Flag_Column=1
Where
Table1.ColumnX=Table2.ColumnX
and
Table1.ColumnY=Table2.ColumunY

Is there a way to do this in Oracle SQL?

My code looks like this:

update Table1
set Flag_Column=1
where ColumnX=
    (select distinct Table1.ColumnX
    from Table1, Table2
    where Table1.ColumnX=Table2.ColumnX
    and Table1.ColumnY=Table2.ColumnY)
and ColumnY=
    (select distinct Table1.ColumnY
    from Table1, Table2
    where Table1.ColumnX=Table2.ColumnX
    and Table1.ColumnY=Table2.ColumnY)

Answer 1

update table1 set flag_column = 1
 where exists (select 1 from table2
                where table1.columnx = table2.columnx
                  and table1.columny = table2.columny)

This will update every row in table 1 where the x, y column combination exists in table2.